What is the Recursive formula for the sequence { 2, 6, 18, 54,...}

Question

A.) a1=2;an=an-1+4

B.) a1=2;an=4an-1

C.) a1=2;an=3an-1

D.) a1=2;an=3an-1+6

Answer 1

I will give you a pattern.

 

2 * 3 = 6

6 * 3 = 18

18 * 3 = 54

 

As you can see, 2 is the first term in the sequence.  Multiplying the current term by the common ratio, which is 3, presents the next term.  Then that term is multiplied by the common ratio to present the term after it.

 

a_{n + 1} = 3a_n

 

or you can write

 

a_n = 3a_{n - 1}

 

where:

a_n is the new term

a_{n - 1} is the preceding term

 

Notice that we can write the following formula as

 

a_n / (a_{n - 1}) = 3

 

This shows that the ratio between the new term to preceding term is 3.